The recombination x-ray laser has been extensively studied because this scheme has potentiality to develop compact x-ray laser. However, most investigations have been made in plasmas under the quasi-steady state approximation. In these plasmas, the population inversion cannot be generated for higher electron density than a certain value. Consequently, the gain for laser oscillation cannot be increased over a limited value. The objective of our project by numerical calculation is to demonstrate that significant improvement in gain performance becomes feasible of the recombination x-ray laser in quite transient (avalanche) recombination of high density plasma in which the quasi-steady state approximation is invalid. An outline of our research results is as follows :An atomic physics code is developed for the avalanche recombination plasma with low-z ions. Time-dependent rate equations for carbon ions were solved in the recombination phase of the fully ionized carbon high density plasma. The initial electron temperature was set to be 10 eV, equivalent to 0.28 eV for the hydrogen plasma. For the electron density higher than 10^<19>cm^<-3> the gain for the C Vl 18.2 nm becomes over 5000cm^<-1>, and increases with the electron density while the duration of population inversion decreases from 1 ps to 10 fs. This shows transient high-gain x-ray laser is feasible due to the avalanche recombination. Charge exchange process between fully ionized carbon ions and helium atoms was also included in the rate equations. The calculation shows that the gain for the CVl 18.2 nm line is as much as 3500cm^<-1> while the corresponding gain without the charge exchange process decreases down to about 200cm^<-1>. This clearly indicates that the charge exchange process plays also a very useful role in producing the avalanche recombination x-ray laser.